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Full text of "Analytical Mechanics"

CHAPTER III.
EQUILIBRIUM  OF RIGID  BODIES.
TRANSLATION AND ROTATION.
32.   Rigid Body.  There are problems in which  bodies cannot be treated as single particles.   In such cases they are considered to be made up of a great number of discrete particles.   A body is said to be rigid if the distances between its particles remain unchanged whatever the forces to which it may be subjected.   There are no bodies which are strictly rigid.   All bodies are deformed more or less under the net ion of forces.   But in most problems discussed in this book ordinary solids may be treated as rigid bodies.
33.   Motion of a Rigid Body.  A rigid body may have < wo distinct types of motion.   When the body moves so that its particles describe straight paths it
is said to have a motion of translation.   Evidently the paths of the particles are parallel, Fig. 20.   If the particles of the body describe circular paths it is said to have a motion of rotation.   The planes of the circles are parallel, while their centers lie on a straight line perpendicular to these planes, which is called the axis of rotation.   The nDBtion of a flywheel is a well-known example of motion of Ijrotation.   Suppose A, Fig. 21, to be a rigid body which is -brought from the position A to the position Af by a motion 5>f2ot&iion about an axis through the point 0 perpendicular e of the paper, then the paths of its particles 30
Fio. 20.